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Improving step complexity for doubly covered polygons and polycubes

Improve the asymptotic number of refolding steps required by the presented algorithms for transforming doubly covered convex polygons and tree-shaped polycubes.

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Background

The paper presents an O(n)-step refolding for doubly covered convex polygons and an O(n2)-step refolding for tree-shaped polycubes.

Determining tighter bounds or optimal algorithms in these settings remains an explicit goal highlighted by the authors.

References

Many open questions remain: Can we improve the number of refolding steps needed for the doubly covered polygon or polycube refolding algorithms?

— All Polyhedral Manifolds are Connected by a 2-Step Refolding (2412.02174 - Chung et al., 3 Dec 2024) in Conclusion